In this note, I introduce a new framework called n-person games with partial knowledge, in which players have only limited knowledge about the aspects of the game -- including actions, outcomes, and other players. For example, playing an actual game of chess is a game of partial knowledge. To analyze these games, I introduce a set of new concepts and mechanisms for measuring the intelligence of players, with a focus on the interplay between human- and machine-based decision-making. Specifically, I introduce two main concepts: firstly, the Game Intelligence (GI) mechanism, which quantifies a player's demonstrated intelligence in a game by considering not only the game's outcome but also the "mistakes" made during the game according to the reference machine's intelligence. Secondly, I define gaming-proofness, a practical and computational concept of strategy-proofness. The GI mechanism provides a practicable way to assess players and can potentially be applied to a wide range of games, from chess and backgammon to AI systems. To illustrate the GI mechanism, I apply it to an extensive dataset comprising over a million moves made by top chess Grandmasters.

翻译：在本文中，我引入了一个名为"部分知识n人博弈"的新框架，其中玩家对博弈的各个方面——包括动作、结果及其他玩家——仅掌握有限信息。例如，实际进行的国际象棋对弈即是部分知识博弈的实例。为分析此类博弈，我提出了一系列衡量玩家智能水平的新概念与机制，重点关注人类决策与机器决策之间的相互作用。具体而言，我引入两个核心概念：其一，博弈智能（GI）机制，该机制通过不仅考虑博弈结果，还根据参考机器智能评估玩家在博弈过程中所犯的"错误"，来量化玩家在博弈中展现的智能水平；其二，我定义了博弈防策略性（gaming-proofness），这是一种兼具实用性与计算性的策略防性概念。GI机制为评估玩家提供了可行方法，并潜在地适用于从国际象棋、双陆棋到AI系统的广泛博弈场景。为说明GI机制，我将其应用于包含顶级国际象棋特级大师超百万步走法的海量数据集。